Tag: How To

Registration for classes in 2018 has been opened. You can find out more about the class schedules here. Do note that JC1 class will commence in first week of January as there are registrations from IP students. For O’levels students, you can treat it like a head-start! We will also be holding a workshop for Post-O’levels Release of Results. So do stay tuned!

Personal Thoughts: The paper isn’t tedious. Students can do them so long as they know their stuffs. There are several generalising of questions, like question 6 of paper 1. We also saw how conditional probability was actually tested subtly, this tests students’ abilities to reason with guidance (not sure if after this first trial year, will they still guide the students.) Application questions were not tough and well guided. Students can solve it easily if they read it well. Statistics was well crafted and neat.

To be blunt, I’ll give credit to the 9740 H2 Mathematics paper that run concurrently, since it is too tough to set two sets of papers. Its easy to acknowledge that the 9740 (2016) paper was way harder than 9740 (2017). Next year won’t be the same.

Advice: Students should be careful when you revise, make sure you learn, and not do. Understand what you’re doing. The 2017 paper was an inquisitive paper, examiners were watching closely if you pay attention to details, and know your definitions well.

I’ll do an analysis for the paper, you can click on the individual question and read. For students that took the paper, I hope it doesn’t demoralise you.

Next, the first derivative test is actually very difficult to administer here. Here’s why… First, the question was to determine, we need to substantiate it fully. One will observe that the equation contains both x and y. Students need to understand that y coordinate can be obtain using . First derivative test suggests we add and minus a small number to x and sub it into , however, students will not be able to figure out if you add or minus a small number to y here. This action assumes the nature of the stationary point. Thus, students are required to do second derivative test here.

Remainder and Factor Theorem will save a lot of time here. I know most of my students that were IP tracks, did long division. This wasted a lot of their time, not to mention if they want to check their workings. This question is a clear indicator that Year 3 and Year 4 topics can and will haunt you. R-Formulae!

Next, the gradient being ALWAYS positive. This tests students on their basic knowledge of differentiation. For starters, is not an increasing function, but it is STRICTLY increasing function. And this makes a lot of difference.

This is a technical question, testing students on their definitions. Very obvious answers, yet most students might struggle with definitions. And of course isn’t really distance since distance is always positive. The more accurate definition is displacement. Then, it was a pure generalisation of our method to solve for the intersection between a line and a plane. Students need to know their stuffs to do this.

This question also paid tribute to the specimen paper, same question number too. ><

First part, had some students cringing, especially those that did long division in question 5. Cos they did long division again. But I always say in class, quadratic equations can be solved with the quadratic formulae.

Next part, is really specific. They want p and q found first, and then using these values found to factorise the equation. You need to follow their instructions, else you will lose credit.

First part, again paying tribute to specimen paper. Very easy, just make sure you simplified.

Second part, is tutorial question, just make sure you simplified.

Last part, some students tried to be smart and suggest is a common ratio, but it is not. Common ratio must be a constant, and this is not. Its just a simple test, use it and show that is less than 1, you’re done. Like I said in previously, question 1 exists to prime students for Q9c. This question actually open up so many possibilities for future sequences and series questions, and I’m very excited.

Simple question, fully guided, just read carefully. Part 2 was neat and tested students’ ability to think out of the box. It is important to note that Q10 and Q6 are the only vectors questions, but all those standard methods to solve for foot of perpendicular, point of reflection, etc were not tested at all. On the other hand, differentiation would have done the trick here. It is interesting since this again open up a lot of possibilities for future questions.

Simple question, fully guided, just read carefully. They could have asked for a graph instead, or even introduce ideas of kinematics from high school. Expect to see more famous scientists appearing in your papers.

General question testing on the formulae for APGP. Solving the polynomial of degree 13 will require the use of the GC, with the graph function. In 2016, we saw a polynomial of degree 10, which could be solved with the {apps}{plysmthz} function. Clearly, more demanding of students’ abilities to use technology now.

(a) is a throwback to high school integration. They didn’t ask for graph too, so the entire question can be solved with a GC. Even finding the intersection between the curves. The definite integral can be solved using {MATH}{9}. No modulus should be applied here. Answer is an exact figure so NO rounding off should be done.

(b) is a bit more challenging. (i) should be manageable, the curve can’t be really be observed, although stronger students might realise they can swap x and y axis in the GC. We simply need to integrate. As we can see from the paper, they blend in the techniques with the applications here. (ii) is slightly intuitive, students should realise that should behave akin to , that is, a constant greater than 1. This is required in order to produce the same shape.

This is a neat question. Some P&C knowledge being tested here, alongside with DRV, ending with a simply binomial distribution. This justifies why P&C is no longer a stand alone topic in this new syllabus, after all, P&C is basic counting principles.

Interesting way to present the questions. (ii) is really specific and students should read really carefully. (iii) is straightforward so long as students are careful that they are dealing with a circle, and its a probability they want.

(a) is very technical. Students need to understand the product moment correlation coefficient to a fair extent. For (i), a downward sloping line will do, just remember to erase the lines since question wants only points. For (ii), a vertical or horizontal line does not give zero correlation, only a square does. (iii) seems easy, but some students might fall into a trap of producing something that is greater than 0.9, make sure you show some zig-zag pattern.

(b) is quite an alright question. The question just wanted students to state the appropriate model, no justification is required, though students should use the r-value to aid them. (iii) is similar to the question asked in H1 Math, so students should be well prepared for it.

Very good question, especially for (vi) – (viii) provide students a good intuition of what conditional probability is all about. Like I shared in class, a simple example: taking the probability of one being pregnant and the test kit indicates you are pregnant, against the probability of one being pregnant given the test kit indicates you are pregnant. This should be fairly intuitively.

Overall, this paper, alongside the specimen paper, should be a good benchmark/ cue for the papers to come. And if its anything, expect more generalisation of questions, more intuitive questions, more cross-topic questions, and more surprises. To students who did not take the paper, you might think the paper was easy, but that might also be because you are guided in class with the paper, or you have the solution. So please do not underestimate the A’levels.

Relevant materials

KS Comments

Students of mine who have been diligently doing the modified TYS I sent them, and have difficulties with the questions that were added in to make the paper a full 3 hour paper, will find the following solutions helpful. Please try to do them in a single 3 hour seating, these are modified to cater to the 9758 syllabus…

The rest of the solutions (that are questions from the original TYS) can be found here.

(iii) is within given data range, and we are performing interpolation, which is a good practice.
The r value is close to 1 which suggest a strong positive linear correlation between the average yields of corn and the amount of fertiliser applied.

(i)
The probability that the lights are faulty is constant.
The event that the light is faulty is independent of another light being faulty.
The light can only be either faulty or non faulty.

(ii)
Let denote the number of faulty lights in a box of 12.

(iii)
Required probability

(iv)
Let denote the number of faulty lights in a carton of 240.

(v)
Events in (iii) is a subset of events in (iv).

(vi)

(vii)
Required Probability

(viii)
From (vii), the quick test seem to be 94% accurate. However, from (vi), we understand that out of the number of lights identified faulty, 42.1% of them will be a mistake. As such, the quick test is not worthwhile, since light identified as faulty are mistakingly discarded. Moreover it will cost money to administer a test.

Relevant materials

KS Comments

Firstly, to do well in this paper, student has to be quite intuitive, to be comfortable with the levels of unfamiliarity.

Q1. Simple expansion using MF26. If you used it carefully, it should provide some guidance to Q9(c) actually.
Q2. Simple graphings, using secondary school modulus function knowledge.
Q3. Students have to know how to use to find back the y-coordinate.
Q4. (a) is even easier if you simply did long division.
Q5. Remainder Theorem from Secondary School for (i). (ii), students need to be alert that when the gradient is ALWAYS positive, the function is strictly increasing, not just increasing.
Q6. Interesting question, that is similar to the Specimen Paper.
Q7. Use of Factor Theorem form MF26 will make this integration much comfortable. By parts work too.
Q8. Standard complex number practice question.
Q9. Very interesting questions. Especially (c), but like mentioned a keen student who did Q1 well, will realise the sum to infinity is simply from MF26.
Q10. Standard vectors questions. Just read carefully and it will be manageable.
Q11. Simple DE too. For the terminal velocity, just need to read that its “after a long time”.

As we are all busy counting down to A’levels, The Culture SG Team will like to share the preparatory course that we have for students.
The lessons will all be $70 for each session and the max class size will be 15 students.

This is a question from TJC Promotion 2017 Question 10. Thank you Mr. Wee for sharing.

Mr. Scrimp started a savings account which pays compound interest at a rate of r% per year on the last day of each year.

He made an initial deposit of $ on 1 January 2000. From 1 January 2001 onwards, he makes a deposit of $ at the start of each year.

(i) Show that the total amount in the savings account at the end of the n year is $ , where .

(ii) At the end of the year 2019, Mr. Scrimp has a total amount of $ in the savings account. Find the value of , giving your answer correct to one decimal place.

Assume that the last deposit is made on 1 January 2019 and that the total amount in the savings account is $50000 on 1 January 2020.

For a period of years, where , Mr. Scrimp can either continue to keep this amount in the savings account to earn interest or invest this amount in a financial product. The financial product pays an upfront sign-up bonus of $2000 and a year-end profit of $200 in the first year. At the end of each subsequent year, the financial product pays $20 more profit that in the previous year.

(iii) Find the total amount Mr. Scrimp will have at the end of years if he invests in the financial product.

(iv) Using the value of found in (ii), find the maximum number of years Mr. Scrimp should invest in the financial product for it to be more profitable than keeping the money in the savings account.